# How do you calculate log_2 (9)?

Apr 9, 2016

Enter it into a calculator. It's about $3.17$.

#### Explanation:

You can change it around a bit, knowing that $9 = {3}^{2}$, so

${\log}_{2} 9 = {\log}_{2} {3}^{2} = 2 {\log}_{2} 3$, but this is a longer way to get to the same answer, and you still have to use a calculator, because you can't do ${2}^{3.17}$ in your head, unless you have a heavy dosage of savant syndrome.

Have decimals in exponents doesn't seem correct. It actually makes more sense as a fraction,

${2}^{3.17} = {2}^{\frac{317}{100}}$

which you can then turn into a root,

${2}^{\frac{317}{100}} = {\sqrt[100]{2}}^{317}$

which is actually what is meant by ${2}^{3.17}$.